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# What is the value of 36x^2 - 108xy + 81y^2?

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Math Expert
Joined: 02 Sep 2009
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What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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10 Aug 2018, 03:50
00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:47) correct 22% (02:11) wrong based on 70 sessions

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What is the value of $$36x^2 - 108xy + 81y^2$$?

(1) $$3y−2x=−4$$

(2) $$x=\frac{5}{y}$$

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What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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Updated on: 10 Aug 2018, 05:03
We need (6x-9y)^2 = 9(2x - 3y)^2

S1: Sufficient

S2: x = 5/y
x = 1, y = 5 --> 2x - 3y = -13
y = 1, x = 5 --> 2x - 3y = 7
Clearly, not sufficient.

Originally posted by sandman13 on 10 Aug 2018, 04:14.
Last edited by sandman13 on 10 Aug 2018, 05:03, edited 1 time in total.
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Re: What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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10 Aug 2018, 05:00
1
1
Bunuel wrote:
What is the value of $$36x^2 - 108xy + 81y^2$$?

(1) $$3y−2x=−4$$

(2) $$x=\frac{5}{y}$$

$$36x^2 - 108xy + 81y^2$$=$$9(4x^2 - 12xy + 9y^2)$$=$$9(3y-2x)^2$$

Re-phrased question stem:- $$9(3y-2x)^2$$=?

St1:- $$3y−2x=−4$$
Sufficient.(substitute the value of 3y-2x in rephrased question stem)

St2:- $$x=\frac{5}{y}$$
Insufficient. (Either value x or y is required)

Ans. (A)
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What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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13 Aug 2018, 07:45

Solution

Given:
• An expression, $$36x^2 – 108xy + 81y^2$$

To find:
• The value of the given expression, $$36x^2 – 108xy + 81y^2$$

Analysing Statement 1
“3y – 2x = -4”
• Squaring on both sides, we get,
o $$4x^2 – 12xy + 9y^2 = 16$$
• Multiplying this equation by 9, we get
o $$36x^2 – 108xy + 81y^2 = 144$$

Therefore, Statement (1) ALONE is sufficient to answer this question

Analysing Statement 2
“x = 5/y”
• Substituting this in the required expression, we get,
o $$180/y^2 – 540 + 81y^2$$
o We cannot find the value of this expression as we do not have any further information about y.

Therefore, Statement (2) ALONE is not sufficient to answer this question

Hence, the correct answer is option A.

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What is the value of 36x^2 - 108xy + 81y^2?   [#permalink] 13 Aug 2018, 07:45
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